Abstract
Assume that $F$ is a nonlinear operator on a real Hilbert space $H$ which is $\eta$-strongly monotone and $\kappa$-Lipschitzian on a nonempty closed convex subset $C$ of $H$. Assume also that $C$ is the intersection of the fixed point sets of a finite number of nonexpansive mappings on $H$. We develop a relaxed hybrid steepest-descent method which generates an iterative sequence $\{x_n\}$ from an arbitrary initial point $x_0 \in H$. The sequence $\{x_n\}$ is shown to converge in norm to the unique solution $u^*$ of the variational inequality \[ \langle F(u^*), v-u^* \rangle \geq 0 \quad \forall v \in C \] under the conditions which are more general than those in Ref. 19. Applications to constrained generalized pseudoinverse are included.
Citation
L. C. Zeng. Q. H. Ansari. S. Y. Wu. "STRONG CONVERGENCE THEOREMS OF RELAXED HYBRID STEEPEST-DESCENT METHODS FOR VARIATIONAL INEQUALITIES." Taiwanese J. Math. 10 (1) 13 - 29, 2006. https://doi.org/10.11650/twjm/1500403796
Information